RNA-specific nucleotidyltransferases (rNTrs) add nontemplated nucleotides to the 3′ end of RNA. Two noncanonical rNTRs that are thought to be poly(A) polymerases (PAPs) have been identified in the mitochondria of trypanosomes – KPAP1 and KPAP2. KPAP1 is the primary polymerase that adds adenines (As) to trypanosome mitochondrial mRNA 3′ tails, while KPAP2 is a non-essential putative polymerase whose role in the mitochondria is ambiguous. Here, we elucidate the effects of manipulations of KPAP1 and KPAP2 on the 5′ and 3′ termini of transcripts and their 3′ tails. Using glycerol gradients followed by immunoblotting, we present evidence that KPAP2 is found in protein complexes of up to about 1600 kDa. High-throughput sequencing of mRNA termini showed that KPAP2 overexpression subtly changes an edited transcript’s 3′ tails, though not in a way consistent with general PAP activity. Next, to identify possible roles of posttranslational modifications on KPAP1 regulation, we mutated two KPAP1 arginine methylation sites to either mimic methylation or hypomethylation. We assessed their effect on 3′ mRNA tail characteristics and found that the two mutants generally had opposing effects, though some of these were transcript-specific. We present results suggesting that while methylation increases KPAP1 substrate binding and/or initial nucleotide additions, unmethylated KPAP1is more processive. We also present a comprehensive review of UTR termini, and evidence that tail addition activity may change as mRNA editing is initiated. Together, this work furthers our understanding of the role of KPAP1 and KPAP2 on trypanosome mitochondrial mRNA 3′ tail addition, as well as provides more information on mRNA termini processing in general.