In Mishnah Yadayim 2:3, we learn that the "first waters" (the first of two splashes of water) poured on the hands while doing ritual hand-washing is tamei (if less than a certain amount), while the hands are tahor. We also see that if after pouring the first waters, you touch your hands to each other, the hands become tamei.
הַיָּדַיִם מִטַּמְּאוֹת וּמִטַּהֲרוֹת עַד הַפֶּרֶק. כֵּיצַד. נָטַל אֶת הָרִאשׁוֹנִים עַד הַפֶּרֶק, וְאֶת הַשְּׁנִיִּים חוּץ לַפֶּרֶק, וְחָזְרוּ לַיָּד, טְהוֹרָה. נָטַל אֶת הָרִאשׁוֹנִים וְאֶת הַשְּׁנִיִּים חוּץ לַפֶּרֶק וְחָזְרוּ לַיָּד, טְמֵאָה. נָטַל אֶת הָרִאשׁוֹנִים לְיָדוֹ אַחַת וְנִמְלַךְ וְנָטַל אֶת הַשְּׁנִיִּים לִשְׁתֵּי יָדָיו, טְמֵאוֹת. נָטַל אֶת הָרִאשׁוֹנִים לִשְׁתֵּי יָדָיו וְנִמְלַךְ וְנָטַל אֶת הַשְּׁנִיִּים לְיָדוֹ אַחַת, יָדוֹ טְהוֹרָה. נָטַל לְיָדוֹ אַחַת וְשִׁפְשְׁפָהּ בַּחֲבֶרְתָּהּ, טְמֵאָה. בְּרֹאשׁוֹ אוֹ בַכֹּתֶל, טְהוֹרָה. נוֹטְלִין אַרְבָּעָה וַחֲמִשָּׁה זֶה בְצַד זֶה אוֹ זֶה עַל גַּבֵּי זֶה, וּבִלְבַד שֶׁיְּרַפּוּ שֶׁיָּבֹאוּ בָהֶם הַמָּיִם:
Hands become unclean and are made clean as far as the joint. How so? If he poured the first water over the hands as far as the joint and poured the second water over the hands beyond the joint and the latter flowed back to the hands, the hands are clean. If he poured the first and the second water over the hands beyond the joint and they flowed back to the hands, the hands remain unclean. If he poured the first water over one of his hands and then changed his mind and poured the second water over both his hands, they are unclean. If he poured the first water over both his hands and then changed his mind and poured the second water over one of his hands, his one hand becomes clean. If he poured water over one of his hands and rubbed it on the other hand it remains unclean. If he rubbed it on his head or on the wall it is clean. Water may be poured over the hands of four or five persons, each hand being by the side of the other, or being one above the other, provided that the hands are held loosely so that the water flows between them.
If the tamei water on one hand can make the other hand tamei by touch, why does it not make tamei the hand it was poured on? I guess that this could just be part of the Rabbinic enactment (since this tumah is entirely Rabbinic), but if so, why not just require a minimum quantity in the first instance, such that no water becomes tamei?