output

zsh:
+zsh:4> command -v xyz
xyz
+zsh:5> unset xyz
+zsh:6> command -v xyz
xyz
+zsh:8> PATH='' 
+zsh:9> command -v xyz
xyz
+zsh:10> PATH=: 
+zsh:11> command -v xyz
xyz
+zsh:12> PATH=. 
+zsh:13> command -v xyz
xyz
+zsh:14> PATH=../t 
+zsh:15> command -v xyz
xyz

ksh:
+ command -v xyz
xyz
+ unset xyz
+ command -v xyz
xyz
+ PATH=''
+ command -v xyz
xyz
+ PATH=:
+ command -v xyz
xyz
+ PATH=.
+ command -v xyz
xyz
+ PATH=../t
+ command -v xyz
xyz

mksh:
+ command -v xyz
xyz
+ unset xyz
+ command -v xyz
xyz
+ PATH=
+ command -v xyz
xyz
+ PATH=:
+ command -v xyz
xyz
+ PATH=.
+ command -v xyz
xyz
+ PATH=../t
+ command -v xyz
xyz

dash:
+ command -v xyz
xyz
+ unset xyz
+ command -v xyz
xyz
+ PATH=
+ command -v xyz
xyz
+ PATH=:
+ command -v xyz
xyz
+ PATH=.
+ command -v xyz
xyz
+ PATH=../t
+ command -v xyz
xyz

bash:
+ command -v xyz
xyz
+ unset xyz
+ command -v xyz
+ PATH=
+ command -v xyz
/home/dualbus/t/xyz
+ PATH=:
+ command -v xyz
./xyz
+ PATH=.
+ command -v xyz
./xyz
+ PATH=../t
+ command -v xyz
../t/xyz

/bin/bash:
+ command -v xyz
xyz
+ unset xyz
+ command -v xyz
+ PATH=
+ command -v xyz
/home/dualbus/t/xyz
+ PATH=:
+ command -v xyz
./xyz
+ PATH=.
+ command -v xyz
./xyz
+ PATH=../t
+ command -v xyz
../t/xyz

busybox sh:
+ command -v xyz
xyz
+ unset xyz
+ command -v xyz
+ PATH=
+ command -v xyz
xyz
+ PATH=:
+ command -v xyz
xyz
+ PATH=.
+ command -v xyz
./xyz
+ PATH=../t
+ command -v xyz
../t/xyz

test

#!/bin/bash

for shell in zsh ksh mksh dash bash /bin/bash 'busybox sh'; do
  echo "$shell":
  $shell <<eof
set -x

xyz(){ :; }
command -v xyz
unset xyz
command -v xyz

PATH=
command -v xyz
PATH=:
command -v xyz
PATH=.
command -v xyz
PATH=../t
command -v xyz
eof
  echo
done

xyz

echo xyz