Hi Ehd123, I did a little bit more research and found this:
Rejection is caused by immune responses to alloantigens on the graft, which are proteins that vary from individual to individual within a species, and are thus perceived as foreign by the recipient. In blood transfusion, which was the earliest and is still the most common tissue transplant, blood must be matched for ABO and Rh blood group antigens to avoid the rapid destruction of mismatched red blood cells by antibodies. Because there are only four major ABO types and two Rh blood types, this is relatively easy. When tissues containing nucleated cells are transplanted, however, T-cell responses to the highly polymorphic MHC molecules almost always trigger a response against the grafted organ. Matching the MHC type of donor and recipient increases the success rate of grafts, but perfect matching is possible only when donor and recipient are related and, in these cases, genetic differences at other loci still trigger rejection. In this section, we will examine the immune response to tissue grafts, and ask why such responses do not reject the one foreign tissue graft that is tolerated routinely the mammalian fetus.
The basic rules of tissue grafting were first elucidated by skin transplantation between inbred strains of mice. Skin can be grafted with 100% success between different sites on the same animal or person (an autograft), or between genetically identical animals or people (a syngeneic graft). However, when skin is grafted between unrelated or allogeneic individuals (an allograft), the graft is initially accepted but is then rejected about 10-13 days after grafting. This response is called a first-set rejection and is quite consistent. It depends on a T-cell response in the recipient, because skin grafted onto nude mice, which lack T cells, is not rejected. The ability to reject skin can be restored to nude mice by the adoptive transfer of normal T cells.
Grafts that are syngeneic are permanently accepted (first panels) but grafts differing at the MHC are rejected around 10-13 days after grafting (first-set rejection, second panels). When a mouse is grafted for a second time with skin from the same donor, it rejects the second graft faster (third panels). This is called a second-set rejection and the accelerated response is MHC-specific; skin from a second donor of the same MHC type is rejected equally fast, whereas skin from an MHC-different donor is rejected in a first-set pattern (not shown). Naive mice that are given T cells from a sensitized donor behave as if they had already been grafted (final panels). When a recipient that has previously rejected a graft is regrafted with skin from the same donor, the second graft is rejected more rapidly (6-8 days) in a second-set rejection. Skin from a third-party donor grafted onto the same recipient at the same time does not show this faster response but follows a first-set rejection course. The rapid course of second-set rejection can be transferred to normal or irradiated recipients by transferring T cells from the initial recipient, showing that graft rejection is caused by a specific immunological reaction. Immune responses are a major barrier to effective tissue transplantation, destroying grafted tissue by an adaptive immune response to its foreign proteins. These responses can be mediated by CD8 T cells, by CD4 T cells, or by both. Antibodies can also contribute to second-set rejection of tissue grafts.
You can find this all here with diagram 
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